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* *Reflection: Developing a Conceptual Understanding
Here Are Your Signs + and - - Section 2: Direct Instruction

*Developing a Conceptual Understanding: Why no independent assignment*

# Here Are Your Signs + and -

Lesson 4 of 11

## Objective: SWBAT be able to understand perform appropriately when shown the addition or subtraction signs.

## Big Idea: Mathematical signs are foreign to most kindergarteners. This lesson requires them to act out addition and subtraction in a informal way so that they can become comfortable with the signs without pressure of performing accurately.

*80 minutes*

Each day we begin our math block with an interactive online calendar followed by counting songs and videos.

**Calendar Time:**

We do calendar on Starfall every afternoon. This website has free reading and math resources for primary teachers. It also has a “more” option that requires paying a yearly fee. The calendar use is free. A detailed description of Daily Calendar math is included in the resources.

**Counting with online sources:** Today we did counting practice to reinforce the counting skills. We watched two to three number recognition 0-10 videos (one to two minutes each) because some of my students students were still struggling with identifying numbers correctly in random order. We watched "Shawn the Train" and counted objects with him to refresh our memories on how to count objects to ten and to reinforce one to one counting. Since we have started the second quarter of the school year, we added to today's counting practice: counting to 20 forward and back, counting by tens to 100 and counting to 100 by ones to get a jump on our end of the year goals.

#### Resources

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#### Direct Instruction

*30 min*

After I give my kids experience with acting out word problems (no paper, no signs, all verbal - see my lesson, Story Problems act it out) I introduce the signs and help them make the connection between the signs and the actions. This is a concept of going macro to micro. I start my addition/subtraction unit with acting out story problems and ending with solving standard algorithms for addition and subtraction.

**For this lesson I use the following materials:**

24 individual snack size bags of snap counting cubes (one color per bag)

Teacher cards with + and - signs

**How to play:**

We review what was learned in the previous lesson(s). We act out a few addition "more" stories and a few subtraction "take away" stories in mixed order. I then have the kids place their blocks on in their bags, hold their hands up in the air (to get their minds off the blocks) and place their hands in their lap.

When everyone is following directions and appear ready to learn, I hold up the + (addition) sign and ask, "Does anyone know what this is?" There is usually at least one who can identify the sign and tell the class what it means.

Student: It's a plus sign.

Me: That's right. Does anyone know another name for this sign? (provide 5 to 6 seconds wait time).

Me: Well, it's what we mathematicians call it an addition sign. What do you think we might do when we see the addition sign?

Student: Usually, at least one of my students able to answer by saying, "put together," "count all the things together," or "get more."

**If a student does not share any helpful information, I provide ideas and clues from what we did while acting out story problems. Such as, "What did we do when there was one rabbit playing and two more came to play?" Once my kids are able to make the connection, I continue with the lesson.

Me: Well, when we are doing addition (getting more or putting things together) we represent it with this sign, the addition sign.

Me: Put your eyes on the whiteboard (I hold a small whiteboard in my hands). I use the board with a dry erase story to draw and write a story problem using the plus sign. "There were 2 frogs sitting on a log. 2 more frogs join them to eat some most delicious flies. How do you think I could show this story on the board?"

Random Student(s): "First, draw a picture of 2 frogs on a log."

Me: I like that idea, but why am I drawing a picture of 2 frogs on a log?

Student (name pulled from a stick jar): Because the story starts with 2 frogs on a log.

Me: Would it be okay if I REPRESENT (emphasis on the vocabulary) the 2 frogs with dots so I don't use too much time drawing? I remember I'm learning how to use an addition sign, not how to draw frogs.

Students: various signs of agreement

Me: I draw 2 large dots on the whiteboard."Okay, here are my 2 "frogs." I am going to write the number 2 under my two frogs. Now what should I do?

Student (name pulled from stick jar): Draw 2 more dots for 2 more frogs.

Me: Why do I want to draw 2 more frogs?

Student (another name pulled from stick jar): Because two more frogs came to eat flies.

Me: "Okay" (I draw 2 more dots for frogs). "Now I am going to write the 2 under those 2 frogs. Now I am going to use the addition sign (+ holding up the sign) in between these two numbers. The board now says, "2 + 2" Can everyone see the addition sign?" Students show a thumbs up once they can locate the + sign on the whiteboard.

Me: This is how you read this problem, "Two plus (plus is another word for addition) two. Read it with me."

Altogether: We read the "Two plus two."

Me: Now I'm going to write the equal sign which means the "same as." (I do not focus on this part very long as this lesson is about becoming familiar with the + and - sign, not about the equal sign. That is in another lesson.)

We do 2 more addition problems in this way and then two or three subtraction problems.

#### Resources

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#### Guided Practice

*10 min*

Once my kids make a connection between the addition sign and "getting more" and the subtraction sign "taking away or putting some back," I have the helper pass out the baggies of snapping counting cubes. For easier supply management, I make sure that students sitting close to each other do not have the same color cubes. This way, I can monitor who is using their tools appropriately and correct those who are not.

I start by asking the kids to put their hands in the air and not touch the cubes until they are told. I then ask them to put their hands in their lap. This helps keep their attention focused on the task, not playing with the cubes.

Me: Okay, when I show you an addition sign, you are going to grab a SMALL handful of cubes out of your bag and lay them on the floor in front of you. If I show the minus sign, you are going to take one or two of the blocks on the floor in front of you (the ones you took out when you saw the addition sign) and you will put them back in your bag.

I call up a high-achieving student to help demonstrate:

"Anelyse, what sign is this? (I show it to Anelyse and the whole class)."

Student: It's an addition sign.

Me: What are you going to do when you see this sign?

Student: I am going to take a small handful of cubes out of the bag.

Me: Please show us. (The student demonstrates.) Good job. Did everyone see that? Now what are you (speaking to whole class) going to do when you see this sign?

Students: Take a some out of the bag.

Me: Very good.

Me to demonstrating student: What are you going to do when you see this sign (subtraction)?

Student: Put some cubes back in the bag.

Me: Why? Turn to your talking partner and tell them why she is going to put some back when she sees this sign.

***Talking partners are pre-assigned for whole-group discussion times using the format below. I draw three random name sticks to share what they discussed with their partners. I accept any answer that makes sense for the concept of subtraction. *

Once we are finished with the demonstration and the kids appear to have a somewhat clear about how the signs are used, we begin the guided practice.

It sounds like this:

Me: I hold up the addition sign.

Students: "get more!" and they reach in their bags and take out a few cubes and place them in front of themselves on the floor.

Me: I hold up the addition sign again.

Students: "get more!" and they take more out of their bags.

Me: I hold up the subtraction sign.

Students: "Take away!" or "Put some back!" and they put one or two cubes back in the bag.

We practice this until there is no hesitation from the students as to what to do when they see the signs.

This activity helps my students clearly understand the use of addition and subtraction signs in kindergarten. Developing and using the correct mathematical vocabulary is Mathematical Practice 6 - Attend to precision. I have found that using an activity like this one helps my students from confusing the signs later when they are solving problems in a number sentence.

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#### Closure

*10 min*

We gather on the floor together and discuss what we thought of the activity and how we could remember what action to take when we see the specific signs.

One student suggests that the plus sign has two lines so we should get more objects when the sign has two lines. We should subtract when their is only one line.

We repeat where we started in the activity:

Me: I show the addition sign and ask, "What is this?"

Students: Addition sign!

Me: What does it mean?

Students: Get more!

Me: I show the subtraction sign. "What is is this?"

Students: Subtraction sign

Me: What does it mean?

Students: Put some back!

**Partner Talk:**

Me: (I hold up the addition sign) Tell your partner what this is and what you do.

Students talk to their partners.

Repeat for the subtraction sign.

I incorporate partner talk in some lessons because it makes the students accountable to someone else to vocalize what they have learned. Research shows that we remember little of what we hear, but a lot of what we see, say and do. Having students talk to a partner increases understanding and use of academic vocabulary.

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#### Exit Ticket

*10 min*

This lesson does not have an explicit Exit Ticket. Instead, I keep notes on things I notice during the activity using an observation form. I look for things like kids who continuously look around for affirmation that they are doing the right thing or appear to have no clue at all (basically, not making a connection between signs and actions).

I record these observations and pull the students into small groups the next day to work through any misunderstandings or lack of understanding of the meanings of the signs.

#### Resources

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- UNIT 1: Make it Count!
- UNIT 2: It All Adds Up!
- UNIT 3: Sorting & Classifying
- UNIT 4: Learning Numbers 11-19
- UNIT 5: Make It Count!
- UNIT 6: Count & Compare
- UNIT 7: Take it Away! (all about subtraction)
- UNIT 8: Know Those Shapes!
- UNIT 9: Subtraction, Subtraction...We all love subtraction!
- UNIT 10: What Makes 10?
- UNIT 11: Same As
- UNIT 12: What Makes 5?
- UNIT 13: How Does It All Measure Up?
- UNIT 14: Fact Families
- UNIT 15: Add It or Subtract It?

- LESSON 1: Story Problems: Act It Out
- LESSON 2: Story Problems: Draw & Do
- LESSON 3: Spin It Addition!
- LESSON 4: Here Are Your Signs + and -
- LESSON 5: The Domino Effect
- LESSON 6: Story Problems: Draw It
- LESSON 7: A Class Book of Addition
- LESSON 8: Flip & Add
- LESSON 9: Treasure Addition!
- LESSON 10: Building Adding & Subtracting Independence
- LESSON 11: Roll & Add